首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Problems of control and information theory (Hungary)
Authors:S Barnett  P Lancaster
Institution:  a School of Mathematical Sciences, University of Bradford, W. Yorkshire, England b Department of Mathematics and Statistics, University of Calgary, Alberta, Canada
Abstract:The bezoutian matrix, which provides information concerning co-primeness and greatest common divisor of polynomials, has recently been generalized by Heinig to the case of square polynomial matrices. Some of the properties of the bezoutian for the scalar case then carry over directly. In particular, the central result of the paper is an extension of a factorization due to Barnett, which enables the bezoutian to be expressed in terms of a Kronecker matrix polynomial in an appropriate block companion matrix. The most important consequence of this result is a determination of the structure of the kernel of the bezoutian. Thus, the bezoutian is nonsingular if and only if the two polynomial matrices have no common eigenvalues (i.e., their determinants are relatively prime); otherwise, the dimension of the kernel is given in terms of the multiplicities of the common eigenvalues of the polynomial matrices. Finally, an explicit basis is developed for the kernel of the bezoutian, using the concept of Jordan chains.
Keywords:
本文献已被 InformaWorld 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号